Which part contains the fractions in ascending order?

### Concept & Strategy To arrange fractions in ascending order (smallest to largest), either convert them into decimal values or analyze the numerical gap between their numerators and denominators. ### Step-by-Step Solution Let's evaluate the approximate decimal value for each unique fraction: * $$\frac{11}{14} \approx 0.785$$ * $$\frac{16}{19} \approx 0.842$$ * $$\frac{19}{21} \approx 0.904$$ Comparing the resulting decimal values: $$0.785 < 0.842 < 0.904$$ Mapping these back to the original fractions: $$\frac{11}{14} < \frac{16}{19} < \frac{19}{21}$$ ### Exam Strategy & Shortcut **Numerator-Denominator Gap Analysis:** Find the difference between the denominator and numerator for each fraction: * For $$\frac{11}{14}$$, the gap is $$3$$. * For $$\frac{16}{19}$$, the gap is $$3$$. * For $$\frac{19}{21}$$, the gap is $$2$$. When the gap is the same (as with $$\frac{11}{14}$$ and $$\frac{16}{19}$$), the fraction with larger numbers is greater. Thus, $$\frac{16}{19} > \frac{11}{14}$$. When comparing fractions with similar numbers, a smaller gap (like $$2$$ for $$\frac{19}{21}$$) generally indicates a fraction closer to $$1$$. Thus, $$\frac{19}{21}$$ is the largest. The correct ascending sequence is $$\frac{11}{14}, \frac{16}{19}, \frac{19}{21}$$. ### Common Pitfall Miscalculating decimal values during long division, especially with prime denominators like $$19$$. Using the gap analysis shortcut saves time and reduces calculation errors. ### Final Answer **Therefore, the correct answer is option (a).**